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Homework Statement
Could someone help point out certain conceptual errors in my interpretation of the mirror clocks time dilation thought experiment? Say S' is the frame of reference traveling at speed V w.r.t to frame S, which means that events happen at the same coordinate in S'.
We know that the measurement of time between the light leaving the source and making a round trip back to the source in this frame is Δt_{0}= 2d/c, where d is the vertical distance between the 2 mirrors. And that the time measured in the nonproper (is this a correct way of putting this?) frame S is Δt = γΔt_{0}, which is in part due to the distance measured between the 2 events VΔt in this frame.
Here's where my understanding becomes messy. If i wished to calculate the distance moved by S', how do I go about doing it? Do I use VΔt? Can i use VΔt_{0} as well (my current understanding is that speed V is identical in both frames after sticking values into Lorentz velocity equations)? If so won't the distance traveled be shorter in the S' frame than the S frame? And how do I interpret these facts?
Thanks for helping!
Homework Equations

The Attempt at a Solution
